Journal of Statistical Physics, Vol. 41, Nos. 5/6, 1985. p. 1037-1044.
Basic assumptions of the capillary wave theory of fluid interfaces are examined critically as a function of space dimensionality d. When the predictions of capillary wave theory are compared with those of the nonclassical Maxwell-van der Waals theory, agreement is found in d = 3 and 4, but strong disagreement occurs in d = 2. It is shown that the total effective mass density obtained from the Hamiltonian describing the collective capillary wave excitations has a logarithmic divergence in d = 2. This result suggests the possibility of anomalous behavior for fluid interfaces in d = 2.